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A Financial Time Reversible Process

In my previous post I extolled the virtues of equilibria and time reversibility.

Take a video of a drop of blood diffusing in water.

Play it backwards.

The video only really makes sense going in one direction.

When the blood has fully diffused, the system is 'in equilibrium', it's in an easier to describe this state than when the blood's diffusing - plus when the system is in equilibrium it's impossible to discern whether the video is being played forwards or backwards.

All we are seeing is murky water.

Asset prices are often assumed to be analogous to such processes on the way to an equilibrium state.

So if we can produce a return time series which from both going long and shorting, perhaps we reduce the characteristic positive drift and negative skewness of stock returns, so that when we look at a return we won't be sure whether we are playing the strategy forward or backwards.

Simply going long and shorting on alternate days achieves this by design.

The skewness of the S&P 500 over 55 years is -1 with an average annualised daily return of +7%.

The Alternating strategy shows a skewness of +0.88 and return of -1.56%.

Interestingly, if one day's return is removed (or hedged away somehow) the skewness changes to -0.24 and 0.09 and returns more or less unchanged. Whatever analysis you are doing, it always pays to do it on a hedged portfolio!

Let's look at skew over time, each day's skew is computed using a year's return history.

Here we see every large loss on the S&P 500 spikes skew downward; whereas with the alternating strategy the chances of being long a large loss day is 50/50.

It is sheer luck that the strategy was long on Black Monday.

In fact I have run several purely random long short strategies which hit upon extremely low skews and drifts. Just luck.

Either way, if I showed you the evil twin of the Alternating strategy - 'Alternating*' - which is Alternating run backwards, you would not be able to tell from the returns that it is indeed run backwards or just 'alternating' on different days. You would have to take my word for it.

This 'petri dish portfolio' has achieved a kind of equilibrium; and by design there is an equal probability that you are seeing the returns running forwards or backwards.

Now we just need to find something interesting to do with our new time reversible property.